Question

1. solve and graph: -5a - 4 > 36 or 3 - 7a ≤ 24

Explanation:

Step1: Solve the first - inequality

Solve \(-5a - 4>36\). Add 4 to both sides: \(-5a-4 + 4>36 + 4\), which simplifies to \(-5a>40\). Divide both sides by - 5 and reverse the inequality sign: \(a<-8\).

Step2: Solve the second - inequality

Solve \(3-7a\leq24\). Subtract 3 from both sides: \(3 - 7a-3\leq24 - 3\), which simplifies to \(-7a\leq21\). Divide both sides by - 7 and reverse the inequality sign: \(a\geq - 3\).

Step3: Graph the solution

For \(a < - 8\), we use an open - circle at \(a=-8\) and shade to the left. For \(a\geq - 3\), we use a closed - circle at \(a = - 3\) and shade to the right.

Answer:

The solution of the compound inequality is \(a < - 8\) or \(a\geq - 3\). On the number - line, we have an open circle at \(a=-8\) with shading to the left and a closed circle at \(a=-3\) with shading to the right.